In the world of baking, precision is not just a recommendation; it is a promise of success. While it may seem like a magical art, pastry is, in essence, a branch of chemistry and physics. And the best place where this is evident is in the most fundamental tool of all: the baking pan. Baking pans, even if they have the same stated size, do not always have the same capacity when they have a different shape. This difference is crucial when aiming for perfection, especially when migrating a recipe from a round pan to a square one or vice versa.

When sharing a recipe, the correct thing to do is to be as specific as possible: indicate the type of pan to use, its diameter or side length, its depth, and its material. Not only do baking times change from oven to oven; even the material and shape of the pans can drastically modify the final result.

The Myth of the Same Size: Why Shape Matters

It is precisely in baking where the most accuracy is needed, both in the weight of the ingredients and in cooking temperatures and volumes, to obtain an exceptional result. This does not imply that if you read a cake recipe that uses a round pan with a 9-inch diameter (23 cm) and you prepare it in a square pan with a 9-inch side (23 cm), the cake will be ruined. But you should know that the batter will not react the same way.

The key lies in capacity: a square pan has more capacity or volume than a round pan with the same base measurement. This is because the corners of the square add a significant amount of area and volume that the circle does not have. Therefore, if you use the same amount of batter in the square pan, the batter will be more spread out and shallower; it will not receive heat in the same way, and although you will surely get a good cake, its height and texture will not be the same as expected in the original recipe.

Homogeneity in making cakes or tarts is the goal of every baker: that is, whenever we follow a recipe, the result should be identically successful. Obviously, we won't always have the exact pan specified in the recipe. That is why it is vital for any beginner or curious baker to know the approximate equivalencies of a round pan and a square pan, and, even more importantly, the mathematical formula to adapt any quantity.

It is calculated that, on average, a square pan has around 25% more capacity than a round pan, assuming both pans have the same depth. This practical rule is the starting point you need.

Quick Guide: Approximate Pan Equivalencies (Square to Round)

If the recipe calls for a round pan and you only have a square one (or vice versa), this guide will help you make a quick decision. Remember that if a recipe calls for a 9-inch (23 cm) round pan, for its equivalent in a square pan, you should use a pan with a side about one inch less (two to three centimeters less).

• 5-inch Square (13 cm) = 6-inch Round (15 cm)
• 6-inch Square (15 cm) = 7-inch Round (17 cm)
• 7-inch Square (17-18 cm) = 8-inch Round (20 cm)
• 8-inch Square (20 cm) = 9-inch Round (22-23 cm)
• 9-inch Square (22 cm) = 10-inch Round (25 cm)
• 10-inch Square (25 cm) = 11-inch Round (27-28 cm)

This chart will save you on many occasions, but if you want perfection, you need the formula we will explain next.

The Master Tool: How to Adapt Ingredient Quantities

When you want to make a cake in a different size or shape than the original recipe, what you are really looking for is a cake that is just as tall and fluffy, but with a different base. This requires changing the amount of batter.

To achieve this, we do not focus on the total volume (which varies by shape) but on the surface area of the base, as this is what will determine how much your batter spreads before rising. The rule is simple: if the surface area of your pan is twice the surface area of the recipe pan, you must double all the ingredients.

Step 1: Calculating the Surface Area (Base Area)

• Circular Pan: It is calculated by multiplying the radius (half the diameter) by itself and by the number pi (π is approximately 3.1416). The formula is: Area = Pi x Radius x Radius.
• Square Pan: Multiply the side length by itself. Area = Side x Side.
• Rectangular Pan: Multiply the longer side length by the shorter side length. Area = Longer Side x Shorter Side.

Step 2: Obtaining the Conversion Factor (The Magic Number)

To calculate the new quantities of ingredients you will need, you just have to apply the conversion factor, which is obtained by dividing the surface area of your pan by the surface area of the pan used in the recipe:

The result of this division is the number by which you must multiply the quantities of absolutely all the ingredients in the original recipe.

Practical Example for a Round Pan

Imagine the original recipe uses a round pan with a 20 cm (8 in) diameter. You want to use a 24 cm (9.5 in) diameter pan.

• Recipe Pan Area (20 cm): Pi x (10 cm)2 is approximately 314 cm2 (Using a 10 cm radius)
• Your Pan Area (24 cm): Pi x (12 cm)2 is approximately 452 cm2 (Using a 12 cm radius)

Applying the conversion factor: Factor = 452 / 314 is approximately 1.44.

This means that for every 100 g (3.5 oz) of an ingredient in the original recipe, you will use $1.44 \times 100 \text{ g} = 144 \text{ g}$ (or $1.44 \times 3.5 \text{ oz} \approx 5 \text{ oz}$). If the recipe calls for 3 eggs, you will use $3 \times 1.44 = 4.32$ eggs (in this case, round to 4 and adjust the liquid). It is a foolproof tool!

The Lifesaving Chart: Quick Multipliers for Round Pans

So you don't have to calculate the radius and Pi every time, this conversion chart already has the areas pre-calculated and gives you the factor by which you must multiply when moving between common circular pan diameters. It's a quick way to apply the basic formula.

A Final Tip for Perfection

• Depth: If you change the capacity, the height of your cake might vary, which affects the baking time. If you use a larger pan and the batter is shallower, reduce the baking time to prevent it from drying out.
• Heat Transfer: Square and rectangular pans have corners that receive more heat than round ones. It's good practice to wrap the corners with damp baking cloth strips (or aluminum foil) to prevent them from overcooking and drying out.

Mastering the science behind pan shapes is not difficult, and by using these formulas and the chart, you will save a lot of time and avoid waste. Happy baking!